1. Field of the Invention
The present invention concerns a channel estimation sequence intended to be transmitted by a transmitter to a receiver via a channel. Such a sequence is for example used in a method of estimating a transmission channel which is also the object of the present invention. The result of this channel estimation method is an optimum estimation of the delays, phases and attenuations of the different paths in the case of a channel with a single path or multiple paths. As will be understood later, this optimum estimation is obtained in a time window with a duration which is determined and which can therefore be chosen when the channel estimation sequence is constructed.
2. Discussion of the Background
In a telecommunications system, the information flows between transmitters and receivers by means of channels. FIG. 1 illustrates a model, discrete in time, of the transmission chain between a transmitter 1 and receiver 2 by means of a transmission channel 3. In general terms, the transmission channels can correspond to different physical media, radio, cable, optical, etc, and to different environments, fixed or mobile communications, satellites, submarine cables, etc.
Because of the many reflections to which the waves transmitted by the transmitter 1 may be subject, the channel 3 is a so-called multipath channel because between the transmitter 1 and receiver 2 there are generally obstacles which result in reflections of the waves propagating then along several paths. A multipath channel is generally modelled as indicated in FIG. 1, that is to say it consists of a shift register 30 having L boxes in series (here L=5) referenced by an index k which can take the values between 1 and L and whose contents slide towards the right in FIG. 1 each time a symbol arrives at its entry. The exit from each box of index k is subjected to a filter 31 which represents the interference undergone and which acts on the amplitude with an attenuation aK, gives a phase shift αk and a delay rK. The output of each filter 31 is then summed in an adder 32. The overall pulse response thus obtained is denoted h(n). This pulse response of the channel h(n) can be written in the form:
      h    ⁡          (      n      )        =            ∑              k        =        1            L        ⁢                  a        k            ⁢              δ        ⁡                  (                      n            -                          r              k                                )                    ⁢              ⅇ                  ja          k                                    where δ(n) representing the Dirac pulse, δ(n−rK) denotes a delay function of the value rK.        
The output of the adder 32 is supplied to the input of an adder 33 in order to add a random signal, modelled by a white Gaussian noise w(n), which corresponds to the thermal noise present in the telecommunications system.
It will be understood that, if the transmitter 1 transmits the signal e(n), the signal r(n) received by the receiver 2 can be written in the form:
                              r          ⁡                      (            n            )                          =                                            e              ⁡                              (                n                )                                      *                          h              ⁡                              (                n                )                                              +                      w            ⁡                          (              n              )                                                              =                                            e              ⁡                              (                n                )                                      *                                          ∑                                  k                  =                  1                                L                            ⁢                                                a                  k                                ⁢                                  δ                  ⁡                                      (                                          n                      -                                              r                        k                                                              )                                                  ⁢                                  ⅇ                                      ja                    k                                                                                +                      w            ⁡                          (              n              )                                                              =                                            ∑                              k                =                1                            L                        ⁢                                          a                k                            ⁢                              e                ⁡                                  (                                      n                    -                                          r                      k                                                        )                                            ⁢                              ⅇ                                  ja                  k                                                              +                      w            ⁡                          (              n              )                                          
The operator * designates the convolution product, defined in general terms by the following equation:
      c    ⁡          (      n      )        =                    a        ⁡                  (          n          )                    *              b        ⁡                  (          n          )                      =                  ∑                  m          =                      -            ∞                                    +          ∞                    ⁢                        a          ⁡                      (            m            )                          ·                  b          ⁡                      (                          n              -              m                        )                              
In order to counteract the distortion caused in the transmitted signal e(n) by the channel 3, it is necessary to determine or estimate at each instant the characteristic of the channel 3, that is to say estimate all the coefficients ak, rk and ak of the model of the channel 3 depicted in FIG. 1. It is necessary to repeat this estimation operation at a more or less great frequency according to the speed with which the characteristics of the channel change.
A widespread method of estimating the channel consists of causing to be transmitted, by the transmitter 1, pilot signals e(n) which are predetermined and known to the receiver 2 and comparing the signals r(n) received in the receiver 2, for example by means of an aperiodic correlation, with those which are expected there in order to deduce therefrom the characteristics of the channel 3 between the transmitter 1 and receiver 2.
It should be stated that the aperiodic correlation of two signals of length N has a total length 2N−1 and is expressed, from the convolution product, by the following equation:
            φ              a        ,        b              ⁡          (      n      )        =                              a          *                ⁡                  (                      -            n                    )                    *              b        ⁡                  (          n          )                      =                  ∑                  m          =                      -                          (                              N                -                1                            )                                                N          -          1                    ⁢                        a          ⁡                      (            m            )                          ·                  b          ⁡                      (                          m              +              n                        )                                              for two signals a(n) and b(n) of finite length N, where the sign to the exponent * denotes the complex conjugate operation.        
The result of the aperiodic correlation operation constitutes the estimate of the pulse response of the channel.
The aperiodic correlation of the signal r(n) received by the receiver 2 with the signal e(n) sent by the transmitter 1 and known to the receiver 2 can therefore be written as follows:φe,r(n)=r(n)*e*(−n)=[e(n)*h(n)+w(n)]*e*(−n)φe,e*h(n)+φe,w(n)φe,e(n)*h(n)+φe,w(n)
In practice the sequence e(n) sent by the transmitter 1 will be chosen so that the autocorrelation φe,e(n) tends towards K·δ(n), k being a real number, and φe,w(n)/φe,e(n) tends towards 0. It is because the aperiodic correlation can then be written:φe,r(n)=k·δ(n)*h(n)+φe,w(n)=k·h(n)+φe,w(n)
Because φe,w(n) is negligible compared with φe,e(n), it is therefore possible to write:φe,r(n)≈k·h(n)
It can then be seen that, having regard to the above hypotheses, the result of the aperiodic correlation of the signal r(n) received by the receiver 2 with the signal e(n) transmitted by the transmitter 1 and known to the receiver 2 constitutes the estimate of the pulse response of the channel 3.
It has been possible to show that there is no unique sequence e(n) for which the aperiodic autocorrelation function φe,e(n)=k·δ(n).